Find frictional force given acceleration, grade, and mass

In summary, the problem involves a 1892kg car moving down a road with a slope of 12% while slowing down at a rate of 3.7m/s^2. To calculate the direction and magnitude of the frictional force, we can use the equation f=ma and the tangent of the angle of the slope. The net force will be parallel to the ramp, and the angle of the slope can be calculated using the tangent function. A free body diagram can help visualize the problem.
  • #1
Butterfly30
28
0
a 1000 kg car is moving down a road with slope (grade) of 15% while slowing down at a rate of 3.7m/s^2 .What is the direction and magnitude of the frictional force?(define positive in the forward direction)


Using f=ma

I have the mass 1000 kg, the acceleration 3.7m/s^2, and slope 15%

Would my force be the tangent of the angle 15??
 
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  • #2
Butterfly30 said:
a 1000 kg car is moving down a road with slope (grade) of 15% while slowing down at a rate of 3.7m/s^2 .What is the direction and magnitude of the frictional force?(define positive in the forward direction)

Using f=ma

I have the mass 1000 kg, the acceleration 3.7m/s^2, and slope 15%

Would my force be the tangent of the angle 15??
Without working the problem, I say no. For one thing the units are incorrect.
 
  • #3
Sorry these were the numbers, I accidently mixed two probs together:/


a 1892kg car is moving down a road with slope (grade) of 12% while slowing down at a rate of 3.7m/s^2 .What is the direction and magnitude of the frictional force?(define positive in the forward direction)


Using f=ma

I have the mass 1000 kg, the acceleration 3.7m/s^2, and slope 15%

Would my force be the tangent of the angle 15??
 
  • #4
So basically given this problem:


a 1892kg car is moving down a road with slope (grade) of 12% while slowing down at a rate of 3.7m/s^2 .What is the direction and magnitude of the frictional force?(define positive in the forward direction)

Would my force be the tangent of the angle 12??
With f=ma
 
Last edited:
  • #5
Butterfly30 said:
Sorry these were the numbers, I accidentally mixed two probs together:/

a 1892kg car is moving down a road with slope (grade) of 12% while slowing down at a rate of 3.7m/s^2 .What is the direction and magnitude of the frictional force?(define positive in the forward direction)

Using f=ma

I have the mass 1000 kg, the acceleration 3.7m/s^2, and slope 15%

Would my force be the tangent of the angle [STRIKE]15[/STRIKE] 12??

The net force will be in a direction parallel to the ramp (down the ramp).

If the ramp makes an angle of θ with respect to the horizontal, then tan(θ) = 0.12 .

Draw a free body diagram.
 

Related to Find frictional force given acceleration, grade, and mass

1. How do you calculate the frictional force given acceleration, grade, and mass?

To calculate the frictional force, you can use the formula F = μmgcosθ, where μ is the coefficient of friction, m is the mass, g is the acceleration due to gravity, and θ is the angle of the grade.

2. What is the role of acceleration in determining frictional force?

Acceleration is an important factor in determining frictional force because it affects the normal force acting on an object. The greater the acceleration, the greater the normal force, which in turn increases the frictional force.

3. How does the grade or incline of a surface affect frictional force?

The grade or incline of a surface affects frictional force by changing the angle of the normal force acting on an object. As the grade increases, the normal force becomes more perpendicular to the surface, resulting in a greater frictional force.

4. What is the significance of mass in calculating frictional force?

Mass plays a role in determining frictional force because it affects the normal force acting on an object. The greater the mass, the greater the normal force, which in turn increases the frictional force.

5. How does the coefficient of friction impact the calculation of frictional force?

The coefficient of friction is a measure of the roughness or smoothness of the surface an object is moving on. A higher coefficient of friction results in a greater frictional force, while a lower coefficient of friction results in a lower frictional force.

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